What is ∞ + ∞ = ????

[Alex K]

Sets don't always contain numbers.  For example, the elements of a power set are sets. To clarify, the infinite set of all positive integers is an element in the power set of the set of all positive integers. Thus, in this instance, we have an infinite element in an infinite set.

Is a countable set more finite than an uncountable set?

What confuses me, is the uncountability of something kind of suggests infinity to me. If you have a truly infinite number of something . . . how can you count it?

I'm guessing they're just math terms. I suck at math.

No no, you just haven't been told what countable means.technically, and its a subtle distinction.

Countable infinite means that you can devise a scheme how to count through the set that will sooner or later reach any arbitrary element of it although.you never finish all of them. You can never finish counting through it because its infinite!, but for any element you choose beforehand you can be sure that it will be reached sooner or later. The simplest example is the integers. 0,1,2,3,4... this counting scheme never ends but will eventually reach any number you want even if you can never finish all of them. This is what countable infinite means.

As opposed to, say, all the real numbers between 0 and 1. There is no way to count through them one by one that ensures that every single one will eventually be reached.